Question: Solve for $y$, $ \dfrac{5}{3y} = -\dfrac{4}{9y} - \dfrac{y - 1}{3y} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3y$ $9y$ and $3y$ The common denominator is $9y$ To get $9y$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ \dfrac{5}{3y} \times \dfrac{3}{3} = \dfrac{15}{9y} $ The denominator of the second term is already $9y$ , so we don't need to change it. To get $9y$ in the denominator of the third term, multiply it by $\frac{3}{3}$ $ -\dfrac{y - 1}{3y} \times \dfrac{3}{3} = -\dfrac{3y - 3}{9y} $ This give us: $ \dfrac{15}{9y} = -\dfrac{4}{9y} - \dfrac{3y - 3}{9y} $ If we multiply both sides of the equation by $9y$ , we get: $ 15 = -4 - 3y + 3$ $ 15 = -3y - 1$ $ 16 = -3y $ $ y = -\dfrac{16}{3}$